[en] We develop a piecewise deterministic control model to study optimal lockdown and vaccination policies to manage a pandemic. Lockdown is modeled as an impulse control that allows the system to switch from one restriction regime of restrictions to another. Vaccination policy is a continuous control. Decisions are taken under the risk of mutations of the disease, with repercussions on the transmission rate. The decision maker follows a cost minimization objective. We first characterize the optimality conditions for impulse control and show how the prospect of a mutation affects the decision maker's choice by inducing her to anticipate the relative benefit of a regime change after a mutation has occurred. Under some parametric conditions, our problem admits infinitely many value functions. We show the existence of a minimum value function that is a natural candidate to the solution given the nature of the problem. Focusing on this specific value function, we finally study the features of the optimal policy, especially the timing of impulse control. We prove that uncertainty surrounding future \bad" vs. \good" mutation of the disease expedites vs. delays the adoption of lockdown measures.
Disciplines :
Systèmes économiques & économie publique
Auteur, co-auteur :
Prieur, Fabien
Ruan, Weihua
ZOU, Benteng ; University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Department of Economics and Management (DEM)
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Optimal lockdown and vaccination policies to contain the spread of a mutating infectious disease
Acemoglu, D., Chernozhukov, V., Werning, I., Whinston, M.: Optimal targeted lockdowns in a multigroup SIR model. Am. Econ. Rev. Insights 3(4), 487–502 (2021)
Alvarez, F., Argente, D., Lippi, F.: A simple planning problem for Covid-19 lock-down, testing, and tracing. Am. Econ. Rev. Insights 3(3), 367–382 (2021)
Aspri, A., Beretta, E., Gandolfi, A., Wasmer, E.: Mortality containment vs. economics opening: optimal policies in a SEIARD model. J. Math. Econ. 93, 102490 (2021)
Bandyopadhyay, S., Chatterjee, K., Das, K., Roy, J.: Learning versus habit formation: optimal timing of lockdown for disease containment. J. Math. Econ. 93, 102452 (2021)
Barrett, S.: Global disease eradication. J. Eur. Econ. Assoc. 1, 591–600 (2003)
Bolzoni, L., Bonacini, E., Soresina, C., Groppi, M.: Time-optimal control strategies in SIR epidemic models. Math. Biosci. 292, 86–96 (2017)
Boucekkine, R., Pommeret, A., Prieur, F.: Optimal regime switching and threshold effects. J. Econ. Dyn. Control 37(12), 2979–2997 (2013)
Boucekkine, R., Carvajal, A., Chakraborty, Sh., Goenka, A.: The economics of epidemics and contagious diseases: an introduction. J. Math. Econ. 93, 102498 (2021)
Caulkins, J., Grass, D., Feichtinger, G., Hartl, R., Kort, P., Prskawetz, A., Seidl, A., Wrzaczek, S.: How long should the COVID-19 lockdown continue? PLoS ONE 15(12), 25 (2020). 10.1371/journal.pone.0243413 DOI: 10.1371/journal.pone.0243413
Caulkins, J., Grass, D., Feichtinger, G., Hartl, R., Kort, P., Prskawetz, A., Seidl, A., Wrzaczek, S.: The optimal lockdown intensity for COVID-19. J. Math. Econ. 93, 102489 (2021)
Choi, W., Shim, E.: Optimal strategies for vaccination and social distancing in a game-theoretic epidemiologic model. J. Theor. Biosci. 505, 110422 (2020)
Crepin, A.S., Naedval, E.: Inertia risk: improving economic models of catastrophes. Scand. J. Econ. 122(4), 1259–1285 (2020)
Cropper, M.: Regulating activities with catastrophic environmental effects. J. Environ. Econ. Manag. 3, 1–15 (1976)
Dasgupta, P., Heal, G.: The optimal depletion of exhaustible resources. Rev. Econ. Stud. 41, 3–28 (1974)
Davis, M.H.A.: Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models. J. R. Stat. Soc. (B) 46, 353–388 (1984)
Di Giamberardino, P., Iacoviello, D.: Optimal control of SIR epidemic model with state dependent switching cost index. Biomed. Signal Process. Control 31, 377–380 (2017)
Dixit, A., Pindyck, R.: Investment Under Uncertainty. Princeton University Press (1994)
Dobie, A.: Susceptible-infectious-susceptible (SIS) model with virus mutation in a variable population size. Ecol. Complex. 50, 101004 (2022)
Dobson, A., Ricci, C., Boucekkine, R., Gozzi, F., Fabbri, G., Loch-Temzelides, T., Pascual, M.: Balancing economic and epidemiological interventions in the early stages of pathogen emergence. Sci. Adv. 9, eade6169 (2023)
Dockner, E.J., Long, N.V.: International pollution control: cooperative versus noncooperative strategies. J. Environ. Econ. Manag. 25(1), 13–29 (1993)
Dockner, E.J., Jørgensen, S., Long, N.V., Sorger, G.: Differential Games in Economics and Management Science. Cambridge University Press (2000)
Eichenbaum, M., Rebelo, S., Trabandt, M.: The macroeconomics of epidemics. Rev. Financ. Stud. 34, 5149–5187 (2021)
Federico, S., Ferrari, G.: Taming the spread of an epidemic by lockdown policies. J. Math. Econ. 93, 102453 (2021)
Federico, S., Ferrari, G., Torrente, M.-L.: Optimal vaccination in a SIRS epidemic model. Econ. Theor. (2022). 10.1007/s00199-022-01475-9 DOI: 10.1007/s00199-022-01475-9
Geoffard, P.-Y., Philipson, T.: Disease eradication: private versus public vaccination. Am. Econ. Rev. 87(1), 222–230 (1997)
Gersovitz, M., Hammer, J.: The economical control of infectious diseases. Econ. J. 114, 1–27 (2004)
Goenka, A., Liu, L.: Infectious diseases and endogenous fluctuations. Econ. Theor. 50, 125–149 (2012)
Goenka, A., Liu, L.: Infectious diseases, human capital and economic growth. Econ. Theor. 70, 1–47 (2020)
Goenka, A., Liu, L., Nguyen, M.: Infectious diseases and economic growth. J. Math. Econ. 50, 34–53 (2014)
Goenka, A., Liu, L., Nguyen, M.: Modeling optimal lockdowns with waning immunity. Econ. Theor. (2022). 10.1007/s00199-022-01468-8 DOI: 10.1007/s00199-022-01468-8
Goldman, S., Lightwood, J.: Cost optimization in the SIS model of infectious disease with treatment. B.E. J. Econ. Anal. Policy 2(1), 1–24 (2002)
Gollier, C.: Pandemic economics: optimal dynamic confinement under uncertainty and learning. Geneva Risk Insur. Rev. 45, 80–93 (2020)
Gollier, C.: Cost-benefit analysis of age-specific deconfinement strategies. J. Public Econ. Theory 22(6), 1746–1771 (2020)
Gracy, S., Paré, P., Sandberg, H., Johansson, K.-H.: Analysis and distributed control of periodic epidemic processes. IEEE Trans. Control Netw. Syst. 8(1), 123–134 (2021)
Huberts, N., Thijssen, J.: Optimal timing of non-pharmaceutical interventions during an epidemic. Eur. J. Oper. Res. 305(3), 1366–1389 (2023)
Jones, C., Philippon, T., Venkateswaran, V.: Optimal mitigation policies in a pandemic social distancing and working from home. Rev. Financ. Stud. 34(11), 5188–5223 (2021)
La Torre, D., Marsiglio, S., Mendivil, F.: Stochastic disease spreading and containment policies under state-dependent probabilities. Econ. Theor. (2023). 10.1007/s00199-023-01496-y DOI: 10.1007/s00199-023-01496-y
Loerstcher, S., Miur, E.: Road to recovery: managing an epidemic. J. Math. Econ. 93, 102482 (2021)
Long, N.V., Prieur, F., Tidball, M., Puzon, K.: Piecewise closed-loop equilibria in differential games with regime switching strategies. J. Econ. Dyn. Control 76, 264–284 (2017)
Martcheva, M.: A non-autonomous multi-strain SIS epidemic model. J. Biol. Dyn. 3(2–3), 235–251 (2009)
Meehan, M., Cocks, D., Trauer, J., McBryde, E.: Coupled, multi-strain epidemic models of mutating pathogens. Math. Biosci. 296, 82–92 (2018)
Okensdal, B., Sulem, A.: Applied Stochastic Control of Jump Diffusions, vol. 498. Springer, Berlin (2007)
Okosun, K.O., Ouifkib, R., Marcus, N.: Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity. Biosystems 106, 136–145 (2011)
Sakamoto, H.: Dynamic resource management under the risk of regime shifts. J. Environ. Econ. Manag. 68, 1–19 (2014)
Tauchen, G.: Solving the stochastic growth model by using quadrature methods and value-function iterations. J. Bus. Econ. Stat. 8(1), 49–51 (1990)
Vermes, D.: Optimal control of piecewise-deterministic Markov processes. Stochastics 14, 165–208 (1985)
